A variety of different types of financial instruments are traded throughout the world. Examples include cash contracts and derivatives. A cash contract is an agreement for either immediate or deferred delivery of the specified asset. A derivative is a financial instrument whose value is linked to the price of an underlying commodity, asset, rate, index, currency or the occurrence or magnitude of an event. Typical examples of derivatives include futures, forwards, options, and swaps.
Most commonly, a swap is an agreement between two parties to exchange sequences of cash flows for a set period of time. Usually, at the time the swap is initiated, at least one of these series of cash flows is benchmarked to an asset or an index that is variable, such as an interest rate, foreign exchange rate, equity price or commodity price. A swap may also be used to exchange one security for another to change the maturity (bonds), quality of issues (stocks or bonds) or to facilitate a change in investment objectives.
A nomenclature has developed to describe the characteristics of certain swaps. A “plain-vanilla” swap is one that only has the simplest and most common terms. A “spot” starting swap is one where the economics of the swap start almost immediately upon two parties entering into the swap. A “seasoned” swap is one that has been in existence for some time. A “forward-starting” swap is one where the first calculation date of the swap does not commence until a designated point in the future. The parties to a forward-starting swap are still responsible for performing their obligations, but these obligations do not start for a period of time after the parties have agreed to enter into the swap. An “off-market” swap is one that has a value other than zero at initiation.
The first swap occurred between IBM and the World Bank in 1981. Although swaps have only been trading since the early 1980's, they have exploded in popularity. In 1987, the swaps market had a total notional value of $865.6 billion; by mid-2006, this figure exceeded $250 trillion. That is more than 15 times the size of the U.S. public equities market.
The most common type of swap is an interest-rate swap. In a plain-vanilla, interest-rate swap, two parties agree to exchange periodic interest payments, typically when one payment is at a fixed rate and the other varies according to the performance of an underlying reference rate. Interest-rate swaps are generally quoted in yield terms. Conceptually, an interest-rate swap can be viewed as either a portfolio of forwards, or as a long (short) position in a fixed-rate bond coupled with a short (long) position in a floating-rate bond. Commonly, for U.S. dollar denominated interest-rate swaps, the rate quoted is the fixed rate that the market expects will offset future 3-month London InterBank Offered Rate (LIBOR) (or whatever underlying reference rate is specified in the swap). (LIBOR refers to a daily reference rate based on the interest rates at which banks borrow unsecured funds from other banks in the London wholesale interbank market.) Cash then flows on a periodic basis between the buyer and the seller depending on the difference between the fixed rate and the floating rate. For example, one party (Party A) agrees to pay another party (Party B) a predetermined, fixed rate of interest on a notional amount on specific dates for a specified period of time; concurrently, Party B agrees to pay Party A a floating interest rate on that same notional amount on the same specified dates for the same specified time period. Interest payments may be made annually, quarterly, monthly or at any other interval determined by the parties.
Standardized derivatives have traditionally been exchange-traded and centrally-cleared financial instruments; swaps, on the other hand, have traditionally been customized financial instruments that are traded in the over-the-counter (OTC) market. (The OTC market most commonly refers to privately negotiated trades between two parties that are not centrally cleared (i.e. uncleared).) Each party looks solely to the other party for performance and is thus exposed to the credit risk of the other party (often referred to as counterparty risk). Unlike financial instruments that are centrally cleared, there is no independent guarantor of performance. Uncleared swaps are often transacted pursuant to International Swaps and Derivatives Association (ISDA) master documentation. The ISDA, 360 Madison Avenue, 16th Floor, New York, N.Y. 10017 is an association formed by the privately negotiated derivatives market that represents participating parties.
It is common for collateral to change hands as the value of an uncleared position changes. The party that has an unrealized loss on an open, uncleared position will post collateral with the party that has the unrealized gain in order to secure its liability. A common form of collateral is obligations of the United States Treasury (i.e. Treasury Bonds, Notes, and Bills). When a Treasury obligation is posted as collateral, price changes in that financial instrument and coupon payments accrue to the owner of the collateral, that being the party posting the financial instrument. Cash may also be posted as collateral, in which case the party receiving the cash as collateral is obligated to pay interest to the party posting the cash collateral at a rate set by agreement between the parties. When the trade is unwound or expires, the party holding the collateral returns it to the other party, and the trade is ultimately settled.
Financial instruments traded on exchanges are distinctly different from uncleared financial instruments. While the economics of the two may be similar, futures and options on futures (futures options) are traded on and pursuant to the rules of an exchange. Unlike uncleared financial instruments where the parties set the terms of the trade, exchange-listed futures and futures options are standardized. Such terms include notional amount, price change per increment, expiration date, and how the financial instrument is settled (either cash settlement or physical delivery) at expiration. The only matters for parties to negotiate in futures, other than which party is the buyer and which party is the seller, is the number of financial instruments to be traded and the price.
All futures and futures options are centrally cleared. This is quite different from uncleared financial instruments discussed above. Central clearing means that the counterparty risk is removed. The parties to a trade cease to be counterparties to each other; rather, each party faces a clearinghouse and looks solely to the clearinghouse for performance. (A clearinghouse is an agency of an exchange or separate entity responsible for settling trading accounts, clearing trades, collecting and maintaining margin, regulating delivery and reporting trading data.)
Recently, there has been a trend for OTC financial instruments to be centrally cleared. In certain circumstances, parties to an OTC financial instrument can submit the financial instruments to a clearinghouse for central clearing. Once the trade is accepted by a clearinghouse, the counterparty risk is eliminated, and each party then faces the clearinghouse. For example, on the Chicago Mercantile Exchange Group's (CME), ClearPort facility, 20 South Wacker Drive, Chicago, Ill. 60606, OTC trades in certain financial instruments may be converted into futures or futures options, as the case may be, upon acceptance by CME's clearinghouse. In effect, these “OTC” financial instruments go through a transformation into futures or futures options. Other financial instruments may be accepted by a clearinghouse for central clearing, but do not convert into futures and remain customized. In these cases, like all centrally-cleared financial instruments, the counterparty risk is still eliminated.
The method by which clearinghouses treat margin on cleared financial instruments (including futures and non-standardized financial instruments accepted for central clearing) is considerably different from the uncleared norm. For both cleared and uncleared financial instruments there are two forms of margin: initial margin and variation margin. For a cleared financial instrument, both parties must post initial margin in an amount set by the clearinghouse upon initiation of a position and maintain that initial margin as long as the position is held. For an uncleared financial instrument, only one party (but not both as in cleared financial instruments) may be required to post initial margin (known as collateral for uncleared financial instruments). In the case of cleared and uncleared financial instruments, a party posting this collateral generally continues to earn interest on cash posted or, if a Treasury instrument is posted, continues to have the right to the coupons generated by the Treasury instrument and accrues the gains or losses from any change in the value of the Treasury instrument.
For variation margin, there is a dramatic difference between the treatment depending on whether the trade is cleared and uncleared. In both cases, margin moves as the marked-to-market value of the position changes. (Marked-to-market value reflects the current value of a financial instrument rather than its book value.) This movement of margin generally occurs on a daily basis. If a party receives variation margin by virtue of a profitable position in a cleared financial instrument, that party is the owner of the margin and may do whatever it chooses with such margin. On the other hand, in uncleared financial instruments, the party posting cash or Treasury instruments as collateral receives the interest on the cash posted or the coupon from the Treasury instrument and accrues the gains or losses from any change in the value of the Treasury instrument (if such a Treasury instrument is posted in lieu of cash).
There are two important effects that result from the difference in the treatment of variation margin between cleared and uncleared positions: the first effect is commonly known as the “convexity bias”, and the second effect will be referred to herein as the “NPV effect”. With respect to the convexity bias, assume a party establishes a short position in a Eurodollar future listed on the CME. Eurodollar futures are based on the 3-month LIBOR interest rate. The final settlement value for Eurodollar futures is equal to 100 minus the 3-month LIBOR rate. As interest rates rise, the price of Eurodollar futures decline. Further assume that shortly after establishing the position, the trade becomes profitable on a marked-to-market basis due to an increase in interest rates. As a result, the party receives variation margin in the form of cash equal to the profit. The party could now use the variation margin to purchase a zero-coupon Treasury bond.
Now assume that interest rates subsequently decline to where they were initially. This results in a payment of variation margin being due—equal to the initial amount received. The party is now in the same position as before the change in interest rates with respect to the futures profit and loss; however, because interest rates are now lower than they were when the zero-coupon bond was purchased, the party will realize a profit on the bond when liquidating it. Hence, there is a clear benefit to being short Eurodollar futures because of the positive correlation between the underlying futures and fixed-income instruments in general. As a result, Eurodollar futures trade at higher yields (lower prices) than related uncleared financial instruments, including interest-rate swaps.
If the underlying asset for the future was natural gas (rather than 3-month LIBOR), then the different treatment of cleared as compared to uncleared collateral schemes would not result in any significant benefit to being short (or long) futures as a result of the convexity bias. This is because there is generally little correlation between the price of a zero coupon bond and the price of natural gas, and the convexity bias only takes effect when such correlation is high.
In the example of Eurodollar futures, the benchmark underlying the future is 3-month LIBOR. There is a very high positive correlation between a zero coupon bond and a Eurodollar future. As first recognized in the early 1990's, this results in a fundamental benefit from being short exchange-traded, interest-rate futures relative to uncleared OTC interest-rate swaps, introducing what is known as a convexity bias in the pricing of interest-rate futures. See Burghardt and Hoskins, “The Convexity Bias in Eurodollar Futures: Part 1”, 1 Derivatives Quarterly 47 (Spring 1995); Burghardt and Hoskins, “The Convexity Bias in Eurodollar Futures: Part 2”, 59 Derivatives Quarterly 72 (Summer 1995). Unless addressed, the convexity bias exists for any financial instrument that is cleared where there is a correlation between the value of the financial instrument and interest rates.
In more detail, as noted by Burghardt and Hoskins: “There is a systematic advantage to being short Eurodollar futures relative to deposits, swaps, or FRAs [Forward Rate Agreements]. Because of this advantage, which we characterize as a convexity bias, Eurodollar futures prices should be lower than their so-called fair or proper values. Put differently, the 3-month interest rates implied by Eurodollar futures prices should be higher than the 3-month forward rates to which they are tied.”
Because there is a high correlation between the yield of an interest-rate swap and interest rates, the convexity bias is highly relevant in determining the value of cleared interest-rate swaps and interest-rate swap futures. The value of the convexity bias is dependent on a number of factors, including the correlation and the volatility of the relevant asset. Under current market conditions, for a convexity biased cleared 10 year dollar denominated vanilla interest-rate swap, the bias is worth approximately 25 basis points (0.25%). It is important to note that when Burghardt and Hoskins first wrote about the convexity bias, interest-rate swaps were not cleared financial instruments.
The second effect that results from the difference between variation margin on a cleared financial instrument and collateral posted in an uncleared financial instrument will be referred to herein as the “NPV effect”. While the NPV effect and the convexity bias are intertwined, cleared financial instruments that have no correlation to interest rates still will be subject to the NPV effect, though not subject to a convexity bias.
The following example illustrates the NPV effect. Assume that a party to a 10-year, natural-gas swap makes fixed monthly payments of $4 (the buyer of the swap), and receives floating payments equal to the spot price of natural gas from a counter party (the seller). Because this is a 10-year swap, these payments continue for 120 consecutive months. Assume further that on the date the swap was created, the 10-year, natural-gas forward curve is flat at $4. Therefore, the swap requires no upfront payments. On the day after the parties enter into the swap, the 10-year, natural-gas forward curve moves to a flat $5. At that point, the buyer expects to receive $1 every month for the next 10 years, or $120 over the next 10 years. The net present value of these cash flows, assuming a 6.0% annual interest rate, is approximately $90. Because of the assumed lack of correlation between the price of natural gas and interest rates in general, the convexity bias does not exist.
In the case of an uncleared natural-gas swap, the buyer receives $90, the net present value of the future cash flows, as collateral from the seller. If the buyer unwinds the trade by selling the swap to a third party for fair value, an upfront payment of $90 will be made to the original buyer, and the $90 collateral will be transferred to the third party. The original buyer has thus realized a profit of $90 and has liquidated its position.
Now consider a cleared natural-gas swap without any adjustments for the NPV effect. When the natural-gas forward curve moves to $5, the fair value settlement price of the cleared swap is $120, the sum of future cash flows. This is because futures by arbitrage-fee principle trade at their future value. Therefore the buyer receives $120 of variation margin today, as opposed to $90 in the uncleared case. The buyer could now exit or hedge off the position, and would be materially better off than had an uncleared swap been traded. This difference is caused by what is referred to herein as the NPV effect. Note that as interest rates approach zero, the NPV effect is eliminated.
Some exchanges and clearinghouses attempt to address this issue by requiring the swap to settle as if it were economically equivalent to an uncleared swap. In this case, the daily settlement price is defined as the net present value of the future cash flows. While this gives the impression that it solves the NPV effect, it does not: this creates a swap that is neither equivalent to a cleared nor an uncleared swap. Continuing with the example, if the swap is required to settle at $90 after the move of the natural-gas forward curve to $5, the buyer receives $90 of variation margin. Now assume that the buyer sells the position to a third party. If the buyer sells the position for the new settlement price, and keeps the $90 of variation margin, then it would be in the same place as if it had traded an uncleared swap. But the new buyer will receive a windfall profit. The new buyer could hedge off the natural-gas price risk by entering into an offsetting, 10-year, $5 natural-gas swap, and receive $30 over the next 10 years. Clearly the existence of this risk-free profit demonstrates that the cleared swap traded at the settlement price of $90 was transacted at something other than fair value. In fact, to consummate the trade at fair value the third party must pay the original buyer the present value of this $30, or approximately $22 under our 6.0% assumed interest rate.
The above example demonstrates that the cleared swap, without an appropriate adjustment, generates a different profit and loss from the uncleared swap when the underlying asset value, the price of natural gas in the example, changes. Furthermore, the example uncovers a potential risk to the clearinghouse that, when the settlement methodologies are not properly delineated, the marked-to-market price may not reflect the actual fair value of the financial instrument. Because central clearing of swaps is relatively new, this effect is not widely known or understood.
The NPV effect also exists with respect to cleared credit default swaps (CDS). In a CDS, the protection buyer makes a series of payments to the protection seller, and in exchange the protection buyer receives a payment if the “reference entity”, usually a corporation or government, defaults. A default includes such events as failure to pay, restructuring, and bankruptcy. In addition to the NPV effect, because of a correlation between the interest rate in general and the default rate a centrally-cleared CDS may have a convexity bias relative to an uncleared CDS. This convexity bias tends to be much smaller than in the case of interest-rate swaps. See, for example, Kaplin, Qu, Wang, Wang, and Zhang, “The Relationship Between Default Risk and Interest Rates: An Empirical Study”, Moody's Analytics (2 Oct. 2009) (available at http://www.moodyskmv.com/research/files/Default_and_Interest_Rates.pdf (accessed 18 Aug. 2010); Chen, Cheng, Fabozzi, and Liu, “An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors”, 43 Journal of Financial & Quantitative Analysis 123 (March 2008) (available at http://www.bnet.fordham.edu/rchen/jfqa-final.pdf) (accessed 18 Aug. 2010).
One attempt to simultaneously address the convexity bias and the NPV effect was the introduction of the “Price Alignment Interest” (PAI) in 2008 on the SwapClear Facility of LCH.Clearnet, Aldgate House, 33 Aldgate High Street, London EC3N 1EA U.K. (LCH.Clearnet is an independent clearinghouse serving exchanges and trading platforms, as well as a range of OTC markets. SwapClear is a service for the central clearing of OTC interest-rate swaps.) Counterparties initially enter into a bilateral interest-rate swap and subsequently submit the swap for clearing through LCH.Clearnet. Upon acceptance of the swap by LCH.Clearnet, the parties to the trade cease to be counterparties to each other and each faces LCH.Clearnet and looks solely to LCH.Clearnet for performance.
LCH.Clearnet introduced PAI to eliminate the convexity bias and the NPV effect. As noted in the LCH.Clearnet rules, “The payment of variation margin, or change in NPV [net present value], on a daily basis without adjustment would distort the pricing for swaps cleared through the Clearing House.” LCH.Clearnet Rule 2C.6.4. To attempt to address this distortion, LCH.Clearnet charges interest on cumulative variation margin received and pays interest on cumulative variation margin paid.
However, PAI is not a viable solution for systems that process cleared financial instruments, including futures. As noted above, variation margin on a cleared position is currently calculated by marking a position to market. This calculation is undertaken on the basis of then-existing market prices, without regard to any convexity bias or NPV effect. The addition of PAI would require the calculation and processing of a separate and distinct form of variation margin. Unfortunately, the systems currently used by traditional futures clearinghouses, exchanges, brokers, and other market participants for calculating variation margin are not equipped to incorporate this additional calculation. Significant changes would be required across the industry to include PAI in the calculation of variation margin for cleared swaps, and it would be very difficult for the industry to adapt to such a methodology in a reasonable time frame.
While swaps have traditionally been uncleared, recently there has been pressure to migrate swaps to central clearing, including mandates set forth in the Dodd-Frank Wall Street Reform and Consumer Protection Act (the “Dodd-Frank Act”) (Pub.L. 111-203, H.R. 4173) signed into law by President Obama on 21 Jul. 2010. As a result of political pressure for greater transparency of uncleared financial instruments, the Dodd-Frank Act was passed into law in the wake of the 2008/2009 financial crisis. During the 2008/2009 financial crisis, many participants in uncleared financial instruments faced counterparties that were unable to meet their obligations.
One such effort to migrate swaps to an exchange and central clearing is the formation of Eris Exchange, an exempt board of trade. As reported by the Financial Times, Eris Exchange “will offer trading in interest-rate swap derivatives closely modeled on current over-the-counter (OTC) rate swaps”. Grant, Weitzman, and Mackenzie, “Chicago Traders Launch New Derivatives Exchange” Financial Times (13 Jul. 2010). The CME's clearinghouse will be the central clearer of interest-rate swap derivatives traded on Eris Exchange. “After the details of the swap, like notional value, coupon, and maturity are agreed to, the Exchange passes the new trade to the Clearing House where it is processed like a traditional futures contract.” http://www.erisweb.com (accessed 17 Aug. 2010).
Unless addressed, the convexity bias and the NPV effect will in most cases result in significant pricing discrepancies between centrally-cleared interest-rate swaps and interest-rate swap futures on the one hand and uncleared interest-rate swaps on the other hand. As a result, the cleared swaps will trade at significantly different yields than the uncleared equivalent. At the very least, the convexity bias and the NPV effect could create a serious impediment to the migration of interest-rate swaps to Eris Exchange, or to any other exchange or to central clearing, including, for example, interest-rate swaps cleared through the International Derivatives Clearing Group, LLC (IDCG), 150 East 52nd Street, 5th Floor, New York, N.Y. 10022 or the CME.
Take the example of an exchange-cleared, $100M, 10-year, interest-rate swap traded at par (i.e. the coupon is set equal to the expected future LIBOR rates over the term of the interest-rate swap). Because this swap is cleared, without an adjustment for the convexity bias, it would it have to be traded at a significantly different yield than an uncleared swap with similar terms or arbitrage opportunities would exist. Assuming that the convexity bias of a 10-year swap is 25 basis points, when the exchange-traded swap trades at a yield of 2.31, the equivalent yield of a traditional, uncleared, interest-rate swap with similar characteristics and terms would be 2.56. In this example, the 25 basis point difference in yields is worth approximately $2,000,000. Furthermore, the NPV effect will create an additional discrepancy between the cleared and uncleared interest-rate swap when the interest-rate yield curve changes such that the fair value of the swap changes. If not addressed properly, these discrepancies resulting from the convexity bias and the NPV effect will create significant confusion and serious impediment to the migration of interest-rate swaps to central clearing and exchange-traded environments.
It would therefore be desirable to offer tools that adequately address the convexity bias and the NPV effect. It would be further desirable to help enable the migration of uncleared swaps and other uncleared financial instruments that are subject to the convexity bias and the NPV effect to exchanges and central clearing to eliminate counterparty risk, whereby the parties to a trade can look solely to a clearinghouse for performance, and to provide for greater transparency.